My schematic will use internal oscillator, but will not require precise timing. It will be produced using surface-mounted ATMEGA328P-AU (in TQFP-32 package). However this is not convenient for prototyping, so I'd like to prototype using ATMEGA328P-PU (in DIP-28 packaging). Will this work in this scenario?
I transferred prototype from Arduino UNO to custom PCB with TQFP-32 without problems. I used Eagle, where I had the scema to create that PCB from scrach, my only problem was, that I use too narrow paths, so while soldering I destroid two pads in vias. Solved it with a piece of copper wire manually riveted in those vias and used as base for soldering, but it does not had anything with CPU. Also created PCB for USB version and worked as expected. I do not see any problems in your way. (If you can create PCB later with different layout ot wires).
You can use/make adapters for breadboards with pins just on two sides, like in Arduino Mini Pro (which is TQFP too) or this one http://www.dx.com/p/elecfreaks-aplomb-boards-tqfp44-32-adapter-board-flower12-for-arduino-green-392511